Fourier-Resolved Spectroscopy of AGN using XMM-Newton data: I. The 3-10 keV band results

0.44 MB·English

by  I. E. Papadakis

To appear in the Astrophysical Journal
Fourier-Resolved Spectroscopy of AGN using XMM-Newton data:
I. The 3-10 keV band results
I.E. Papadakis1,2, Z. Ioannou2,1, D.Kazanas3
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ABSTRACT
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2

n We present the results from the Fourier Resolved Spectroscopy of archival
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J XMM-Newton data of five AGN, namely, Mrk 766, NGC 3516, NGC 3783, NGC

9 4051 and Ark 564. This work supplements the earlier study of MCG-6-30-15
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as well as those of several Galactic Black Hole Candidate sources. Our results

1
exhibit much largerdiversity thanthoseofGalacticsources, afactweattributeto
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9 the diversity of their masses. When we take into account this effect and combine
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our results with those from Cyg X-1, it seems reasonable to conclude that, at
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1 high frequencies, the slope of the Fourier-resolved spectra in accreting black hole
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systems decreases with increasing frequency as ∝ f−0.25, irrespective of whether
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0 the system is in its High or Low state. This result implies that the flux variations
/
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in AGN are accompanied by complex spectral slope variations as well. We also
p
- find that the Fe Kα line in Mrk 766, NGC 3783 and NGC 4051 is variable on
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r time scales ∼ 1 day – 1 hour. The iron fluorescence line is absent in the spectra
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s of the highest frequencies, and there is an indication that, just like in Cyg X-1,
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: the equivalent width of the line in the Fourier-resolved of AGN decreases with
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i increasing frequency.
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a Subject headings: Galaxies: Active, Galaxies: Seyfert, X–Rays: Galaxies
1. Introduction
OurgenericnotionofthecentralengineofActiveGalacticNuclei(AGN)and,ingeneral,
also that of compact Galactic sources such as neutron stars and black holes powered by
1Physics Department, University of Crete, Heraklion, 71003, Crete, Greece
2IESL, Foundation for Research and Technology-Hellas,711 10 Heraklion,Crete, Greece
3Laboratory for High Energy Astrophysics, NASA, Goddard Space Flight Center, Code 661, Greenbelt,
MD 20771,USA
– 2 –
accretion, involves a geometrically thin, optically thick accretion disk that emits locally
as a black body “sandwiched” between a hot (∼ 109 K) corona which up-Comptonizes the
disk thermal radiation to produce the ubiquitous X–ray emission associated with this class of
objects. Despitethecompellingtheoreticalargumentsinsupportofthispicture, independent
supporting evidence of the specific geometrical arrangement is hard to come by. For one,
only a small fraction of the very broad band multicolor black body spectrum of the putative
disk is covered by our instruments making hard the detailed assessment of the form of its
spectrum. Second, the Comptonization spectrum of the hot corona provides information for
only the integral of the Comptonization parameter along our line of sight, rather than the
conditions of the local plasma.
Independent support of the above generic picture has been sought in distinct spectral
and timing signatures implied by the specific geometric arrangement. More specifically, the
Fe Kα fluorescence line at E = 6.4 keV as well as the so-called reflection ‘hump’, the product
of reprocessing the X–rays of the hot corona by the matter of the underlying accretion disk,
are thought to provide a direct measure of the above geometry. Furthermore, the Keplerian
motion of the reprocessing matter in the disk would lead to a rather broad profile for this
spectral feature. Indeed, the detection ofsuch a featureinthe ASCA spectra of many Seyfert
galaxies (e.g. Nandra et al. 1997) seems to provide a confirmation of these notions. At the
same time it has been argued that detailed X–ray spectroscopy of the iron line emission
features can provide information on the location and kinematics of the cold material within
a few gravitational radii of the event horizon.
In addition to the above features, a measure of the size of the X–ray emitting region,
independent of its spectral properties, can be obtained from time variability studies. In
the specific case of emission produced by the Comptonization process, Kazanas, Hua &
Titarchuk (1997) argued that timing observations are the only way to estimate the density
of the emitting plasma (in contrast to its column density provided by the Comptonization
spectra) and thus peek into the dynamics of the accretion flow. The principal method of
characterizing the variability of accretion powered sources has been the measurement of the
Power SpectralDensity function(PSD)oftheirX–raylightcurves, whichinthecaseofAGN,
were shown to be simple power laws with occasional “breaks” in the slope at sufficiently low
frequencies. However, unlike the Comptonization spectra whose slopes and cut-offs can be
related directly to the physical parameters of the emitting plasma, there is no simple model
that relates in a direct fashion the shape of the PSD to the physics of the accretion flow.
Recently, a novel approach in the study of accretion powered sources, which combines
variability and spectral information, has been taken by Revnivtsev, Gilfanov & Churazov
(1999). Using RXTE data, they measured the power spectrum, and hence the amplitudes
– 3 –
of the Fourier components, of Cygnus X-1 in its hard state for different energies. Then, at
each energy band, they assembled the Fourier amplitudes within a given Fourier frequency
range, say ∆f, to produce the so-called Fourier-Resolved (FR) spectrum of the band ∆f.
The process was repeated to obtain the FR spectra of many such frequency bands, thereby
combining theinformation provided by the time variabilitywith the simplicity of theinsights
provided by the “energy spectra”. Their main conclusions were that: (a) the soft component
of the spectra (thought to represent thermal emission from the innermost parts of the accre-
tion disk) is absent from the Fourier resolved spectra, indicating that it is not variable on
time scales less than ∼ 100 s, (b) The FR spectra (in the frequencies that are determined)
are power-laws which become progressively harder with increasing Fourier frequency, and (c)
the Fe Kα line and reflection components become less pronounced as the Fourier frequency
increases.
Using the same approach, the X–ray continuum spectral variability of the Galactic
black hole binaries (GBHs) GX 339-4 and 4U 1543-47, during its 2002 outburst, as well
as Cyg X-1 in its soft state have also been studied respectively by Revnivtsev, Gilfanov
& Churazov (2001); Reig et al.(2006), and Revnivtsev, Gilfanov & Churazov (2000). The
Fourier-resolved spectroscopy (FRS) has also been used to study the nature of the quasi-
periodic oscillations in neutron stars (Gilfanov, Revnivtsev, & Molkov 2003, Gilfanov &
Revnivtsev 2005; Sobolewska & Z˙ycki 2006).
Recently, Papadakis, Kazanas, & Akylas (2005) applied for the first time the same
technique to an AGN, namely to the XMM-Newton observations of MCG -6-30-15. Their
results were similar to those of Revnivtsev et al. (1999) in the case of Cyg X-1 in its hard
state, with the exception of the soft excess component at energies E<1 keV which was
∼
present in the spectra of all Fourier bands, implying variability of this component in all
frequency bands examined, in contrast with the behavior of Cyg X-1.
In the present note we apply the method of Fourier-resolved spectroscopy to five more
AGN, using observations by XMM-Newton. Our aim is to explore the spectral variability
properties of a sizable sample of AGN, as implied by the application of FRS, in order to
investigate whether potential common trends and similarities with GBHs. In this work
we report our results regarding the AGN spectral variability properties at energies above
3 keV. In this energy band, the AGN time-average spectra are dominated by a power-law
continuum. Reflection features like the iron Kα line, and the associated absorption edge,
appear as well. At lower energies, many AGN show considerable complexity, caused either
by the presence of warm absorbing material and/or by the presence of the so-called soft-
excess emission component. In principle, the warm absorber can respond to variations of
the underlying continuum while the soft excess emission is often observed to be variable.
– 4 –
Consequently, FRS can be used in order to study in detail their variability properties. We
plan to present the results from such a study in the near future.
In §2 and §3 we discuss the data sets and the methodology we use, respectively. In §4
we present the results from various model fits to the time average and FR spectra of the
objects in our sample. Finally, in §5 and §6 we discuss our results briefly in the context of
theoretical ideas and models presently in the literature and we present our summary and
future plans, respectively.
2. Observations & Data Reduction and Analysis Method
XMM-Newton, with the large effective area of its instruments and its capability to
observe a source continuously for a period up to ∼ 1.3 days, can provide long duration
light curves that are appropriate in order to obtain accurate Fourier-resolved spectra for
the AGN. To this end, we searched the XMM-Newton public data archive for those AGN
which have been observed, at least once, for an on-source exposure time larger than 100
ks. Prior to April 2005, there were 5 AGN which satisfied this criterion, namely Mrk 766,
NGC 3516, NGC3783, NGC 4051, and Ark 564. For those objects, we also considered all the
available observations in the archive, as in principle we can combine the data from different
observations in order to estimate the FR spectra as accurately as possible.
Apart from the criterion regarding the exposure time, we also required that the objects
show significant variations in all the energy bands that we consider (see below). For this
reason, we used 1000 s binned light curves (in this way the source counts in each bin were, on
average, larger than 20) and applied the usual χ2 test. We found that all sources displayed
variations significant at more than the 95% confidence level, in all energy bands, except
from the November 2001 observation of NGC 3516. Significant variations can be detected
during the April 2001 observation of this source. Although the on-source exposure time in
this case is smaller than 100 ks, we decided to keep the source in our sample and use the
data from this observation to study its FR spectra. As for the shorter observations of the
other sources, none of them showed significant variations, except from the November 2002
observation ofNGC4051. Infact, thetime-average spectra of thesource during the 2001and
2002 observations are so different that we decided to study the two FR spectra separately.
In Table 1 we list the details of all the observations that we have used in the present
work. All data have been reduced using XMMSAS v6.1.0. We use data from the European
Photon Imaging Camera (EPIC) pn detector only. All sources were observed on-axis. With
an average count rate of less than ∼ 30 cts s−1 in all cases, photon pile-up is negligible
– 5 –
for the PN detector, as was verified using the XMMSAS task epatplot. Source counts were
accumulated using a circular region of 40′′ around the position of the source. Background
data were extracted from a similar size, source free, region on the chip. We selected single
and double pixel events (PATTERN=0−4) in the energy range from 200 eV to 10 keV.
The background was in general low and stable throughout all the observations, with the
exception of short periods at the start and/or at the end of each observation. Data from
these periods of high background levels were removed. The “exposure times” listed in the
third column of Table 1 refer to the total on-source exposure time of the pn detector, after
these high background level periods are removed.
In Figures 1 and 2 we show the 0.2−10 keV, background-subtracted, 100 s binned light
curves, extracted from the data of all observations that we consider in this work. All light
curves are normalized to the lowest count rate observed. In this way, one can easily judge
their “quality”. For example, NGC 3516 shows the smallest amplitude variations (min-to-
max amplitude ratio of ∼ 1.5−1.6). Its light curve is also short, and of low signal-to-noise
ratio. On the other hand, NGC 4051 shows the largest amplitude variations (with a min-to-
max ratio of∼ 15 during the 2001observation). The longest light curve is that of NGC 3783.
This source is bright, and also displays significant variations on all sampled time scales, with
a maximum amplitude of ∼ 2.5.
3. Analysis Method
In this section we present in some detail the theory on which FRS is based, as this is
still a novel analysis method, rarely used in the variability studies of compact objects. The
method is based on the fact that any stationary process can be represented as the “sum” of
sine and cosine functions (e.g. Priestley 1989). More specifically, let us denote with X(t)
a stationary process, i.e. the time variable emitted flux from an AGN, for example. Then,
X(t) can be represented as,
+∞ +∞
X(t) = cos(ωt)dU(ω)+ sin(ωt)dV(ω).
Z0 Z0
Theintegralsabovearestochasticanddefinedinthemean-squaresense(Priestley 1989).
As for the stochastic processes dU(ω) and dV(ω), they are orthogonal (i.e. their increments
at different frequencies are uncorrelated) and, more importantly, for each frequency, ω, one
can write,
h|dU(ω)|2i = h|dV(ω)|2i = h(ω)dω,
– 6 –
where the brackets denote the mean of a random variable, and h(ω) is the (non-normalized)
power spectraldensity functionofthestationaryprocessX(t). Inotherwords, theamplitude
of the sine and cosine (random) functions that can be used to represent X(t) are related
to the power spectral density function of X(t). This is the ‘crucial’ property that we can
use in practice to estimate the amplitude of the sine and cosine functions (i.e. the “Fourier
components” of the random process under study).
Suppose we observe the X–ray emission from an AGN N times over a period of T
s. Let us denote with ∆t the interval of each observation (so that N∆t = T), and with
x(E,t )(i = 1,2,...,N) the N points of the light curve (in units of counts s−1). Note that
i
we have assumed we observe the object at a particular energy band of (median) energy E.
Using the discrete Fourier-transform of the light curve, we can estimate the power spectral
density function (PSD) of the random process (whose one realization is the light curve at
hand) as follows,
2
N
2∆t
P(E,f ) = x(E,t )e−2πfjt . (1)
j i
N
(cid:12) (cid:12)
(cid:12)Xi=1 (cid:12)
(cid:12) (cid:12)
(cid:12) (cid:12)
The units are (counts s−1)2 Hz−1, and(cid:12)the PSD is estima(cid:12)ted at the set of frequencies,
f = j/T,j = 1,...,N/2. Based on what we mentioned above, the quantity,
j
R(E,f ) = P(E,f )∆f (countss−1), (2)
j j
q
(where ∆f = 1/T) can be considered as an estimate of the amplitude of the Fourier compo-
nents with frequency f .
j
Suppose now that we have obtained N light curves at different energy bands with
E
median energy E ,k = 1,2,...,N . If, for each one, we estimate the amplitude of the
k E
Fourier components with frequency f , i.e. R(E ,f ), then the plot of R(E ,f ) as a function
j k j k j
of energy, constitutes the “energy spectrum of the amplitudes of the Fourier-component with
frequency f ”, or the “Fourier-resolved spectrum at frequency f ”.
j j
Although some of the objects we study in this work are quite bright (for AGN), it is
not possible to study their FR spectra using the full energy resolution offered by XMM-
Newton. Instead, for each object we extracted light curves in seven bands from 3 to 7 keV
with ∆E = 0.5 keV, and also the 7−8 and 8−10 keV bands, using a bin size of 100 s. We
corrected for the background contribution, estimated the power spectrum (using equation
1), and then subtracted the contribution of the Poisson noise.
– 7 –
In all objects, many of the P(E ,f ) values, after the subtraction of the Poisson noise,
k j
are negative, especially at the highest energies and frequencies. As a result, the estimation
of the respective R(E ,f ) is not possible. For this reason, we considered two frequency
k j
ranges, namely 10−5 −5×10−4 Hz and 5×10−4 −1×10−3 Hz (hereafter the “LF” and “HF”
bands). First we estimated the average of the power spectrum estimates in each band, and
then we used equation (2) to estimate the average amplitude of the Fourier components in
the respective band.
Thefrequencyrangesthatweconsiderareverybroad. TheLFandHFbandscorrespond
to Fourier components with periods from 105 to 2×103 s and 2×103−1000 s, respectively.
This is necessary in order to estimate, as accurately as possible, the average amplitude of the
Fourier components, especially in the higher energy bands. However, this choice unavoidably
affects the accuracy of the errors of the FR spectra. The error estimation of the average
Fourier amplitudes is based on the scatter of the individual amplitudes around their mean
in each frequency band. However, due to the red noise character of the AGN power spectra,
this scatter is representative, to some degree, of the intrinsic, power-law like dependence of
the Fourier amplitudes on frequency. Consequently, the estimated errors of the FR spectra
are expected to be overestimated. This effect should depend on the power spectrum slope
of each individual source, and is expected to affect more the LF band estimates. In §4 we
discuss how we addressed this issue during the FRS model fitting process.
3.1. Interpretation of FRS
The past few years, plots of the energy-dependent variance, σ2, or the rms fractional
E
variability, i.e. r = σ /hx i (where hx i is the average count rate) as a function of E have
E E E E
become increasingly popular in the study of the spectral variability properties of AGN and
GBHs (see for example Edelson et al. 2002, Taylor, Uttley & McHardy 2003, and Markowitz,
Edelson & Vaughan 2003 for the application of this method in X–ray variability studies of
AGN). Roughly speaking, the variance is equal to the integral of the power spectrum of
the source, i.e. σ2 = ∞ P(E,f)df, where T is the length of the observed light curve. In
E 1/T
practice, this integral can be approximated by the sum: P(E,f )∆f = R2(E,f ).
R j j j j
Consequently, the “rms vs. E” plots and FRS are related analysis methods.
P P
In effect, FRS “decomposes” the rms in each energy band into the contribution of the
individual Fourier components. Obviously, the FR spectra provide “more” information, in
the same way that a power spectrum provides “more” information than just the variance of
a light curve. However, while the variance can be estimated “easily”, the requirements for
an accurate estimate of the power spectrum are much more demanding. The same is true
– 8 –
for FRS and the“rms vs E” plots. We need longer, and high signal-to-noise light curves in
order to perform Fourier-resolved spectroscopy, while a rough estimate of the “rms vs E”
plot can be achieved with lower quality data.
Although the units of the Fourier-resolved spectra are the same as those of the observed
energy spectrum, they cannot be interpreted in the same way. While the energy spectrum
exhibits the distribution of the emitted flux as a function of energy, the Fourier-resolved
spectrum provides the amplitude of variability in a certain frequency range, say ∆f, as a
function of energy. Furthermore, while the integral of the energy spectrum over a certain
energy range, say ∆E, is equal to the power emitted from the source over that energy band,
the integral of the Fourier-resolved spectrum is equal to the contribution of the Fourier
components, in the frequency range ∆f, to the variance of the light curve in the energy
band ∆E. Consequently, the use of the word “spectrum” for a “R(E,f) vs E” plot can be
misleading. We will keep using this term though, as this is what has been used in the past
and a change of terminology may cause confusion. However we emphasize again that the
Fourier-resolved spectra do not show how photons are distributed as a function of energy.
They simply show how the variability amplitudes, at a certain frequency, change with energy.
So, what is the use of these “spectra” in practice? Their important property is that
they receive contribution only from the spectral components which are variable on the time
scales sampled by the observations. For example, let us consider the case of an AGN with
a power-law (PL) X–ray continuum of slope Γ. Suppose now that apart from this PL
component, other spectral components (like e.g. reflection from a cold or ionized disk and/or
heavy absorption by warm material) also appear in the time-average spectrum of the source.
Becauseofthepresence ofsuchcomponents, sometimeitisdifficult todetermineΓ. However,
if only the PL component varies in normalization, then, as we show in the Appendix, the
Fourier-resolved spectra will have a power-law shape of slope Γ, at all frequencies. Hence,
in this case, the FR sectra can not only show the variable component, but provide also an
accurate estimation of Γ as well.
A straightforward utility of FRS is found in the study of spectral features that result
from reprocessing of the continuum since in this case there exist a natural filter (the light
crossing time) which filters out all frequencies higher than ∼ R/c (R is the size of the
reprocessing area and c the speed of light). Such a feature could be an emission line at
energy, say E , produced by continuum reprocessing over a region of size R. Should its
0
normalization vary in proportion to the underlying continuum at a given frequency, its EW
should remain constant for frequencies ν<R/c while it would be vanishing for ν>R/c.
∼ ∼
Lower EW values at a certain frequency range will imply that the line is not “as variable”
as the continuum on the respective time scales, either because of the light crossing argument
– 9 –
or because the physical condition at the corresponding radius do not favor the presence of
the associated transition.
In summary, the Fourier-resolved spectra can show us clearly if and, most importantly,
how the various spectral components in the overall energy spectrum of a source vary on the
frequency ranges considered. The easiest way to accomplish this, in our case, is to perform a
standard model fitting analysis to the FR spectra in the LF and HF bands and then compare
the results with those obtained from a similar analysis of the time-average energy spectrum.
The model fitting to the time-average spectrum can identify the spectral components which
contribute to the emitted radiation from the source. The results from the model fitting of
the FR spectra will identify which one of the individual spectral components is variable. Any
differences between the best fitting parameter values of the time-average spectrum and the
LF/HF FR spectra will give us information as to how the respective spectral components
vary.
We discuss below the results from the application of this method to the data of the five
AGN we study in this work.
4. Spectral Analysis & Model Fits
The spectral model fits have been performed with the XSPEC v11.3 package. The errors
on the best-fitting model parameters that we report represent the 1σ confidence limit for one
interesting parameter. The energy of the emission and absorption features are given in the
rest frame of the source. Since the number of points in the mean energy spectrum and the
FR spectra is small, whenever possible, we performed the model fitting with the parameters
of the emission or absorption features kept fixed at “sensible” values (i.e. at 6.4 keV for the
iron Kα line and 7.1 keV for the associated absorption edge).
We consider a model as providing an acceptable fit to the data if the null hypothesis
probability islargerthan5%. Weaccept thattheadditionofamodelcomponent isnecessary
if the quality of the model fitting is improved at more than the 95% significance level. All
spectral fits include Galactic absorption, with column values taken from Dickey & Lockman
(1990). They are listed on the top of the Tables where we report our best fitting model
parameter values.
Spectral responses and the effective area for the pn spectra were generated with the
SAS commands rmfgen and arfgen. Since both the time-average and the FR spectra have
a much coarser energy resolution than the intrinsic resolution of the EPIC pn detector, we
used the FTOOLS command rbnrmf to rebin the original pn response matrix accordingly.
– 10 –
Furthermore, a uniform systematic error of 1% was added quadratically to the statistical
error of the time-average spectra to account for all the systematic uncertainties that may be
introduced when we undersample the original energy resolution of the instrument and use a
“binned” response matrix.
This systematic error was not added to the Fourier-resolved spectra, since as we men-
tioned above their errors are probably overestimated anyway. In order to resolve this issue
we followed a model-dependent procedure. We fitted each FR spectrum with a simple power-
law model in the energy bands 3−5.5 and 7−10 keV. In most cases, the resulting reduced
χ2 values, χ2, were significantly smaller than 1. We would then reduce the errors by an
ν
appropriate factor (equal to ∼ 2−5 and ∼ 1.5−4.5 in the case of the LF and HF spectra,
respectively) so that χ2=1. The resulting error-correction factors were then applied to the
ν
5−7 keV band points as well.
4.1. Mrk 766
The time-average spectrum and the LF/HF FR spectra of Mrk 766 are plotted in the
upper panel of Figure 3 (open circles, filled squares and filled triangles, respectively). The
mean spectrum is well fitted by a power law model of Γ ∼ 2.15 and a broad Gaussian line
av
with E ∼ 6.45, σ ∼ 480 eV and EW ∼ 230 eV. The best fitting model is shown with
line,av av
the dashed line in the upper panel of Figure 3 and the best fitting model parameter values
are listed in Table 2. They are in good agreement with the results from the same model fit
to the full energy resolution EPIC pn spectrum (see §3.2 in Pounds et al. 2003).
In the lower three panels of the same Figure we plot the Data/Model ratio in terms of
“sigmas” (i.e., the error of each point; as a result, the errors of the points in these plots are of
size one). In the case of the time-average spectrum, “Model” refers to the best fitting model
(with the parameter values listed in Table 2) while in the case of the LF and HF spectra, as
“Model” we use the best PL model fit.
The HF spectrum appears to be rather noisy but a PL model (Γ ∼ 1.9) fits it rather
HF
well. The LF spectrum is also well fitted by a simple PL model (Γ ∼ 2.2, χ2/degrees of
LF
freedom (dof)=11.4/8). However, when we add a narrow Gaussian line (i.e. σ kept fixed at
100 eV) with E “frozen” at 6.45 keV (the best fitting value in the case of the time-average
line
energy spectrum) we find that χ2/dof =5.5/7. According to the F-test, the addition of the
narrow line is significant at the 97.1% level.